Human Acitivity Recognition
Manav Sehgal
1/31/2018
Executive Summary
This data contains data from accelerometers on the belt, forearm, arm, and dumbell of 6 participants. Mostly for each sensor it contains the angle, avg, standard deviation, variance, kurtosis, skewness, amplitude, min and max for each of the rotation angles - pitch, roll, yaw. In addition is also contains the gyro, accel and magnetometer reading in each direction.
We tried 3 different models for prediction -** 1) Decision Tree, Random Forest without PCA, 3) Random Forest with PCA.**
Of the three models, we got a 98% accuracy with Random Forest without PCA model on training and 100% accuracy on the validation data - highest among all three and was used for predictions on the test data set.
Analysis Overview
Devices such as Jawbone Up, Nike FuelBand, and Fitbit it is now possible to collect a large amount of data about personal activity relatively inexpensively.In this project, the goal is to use data from accelerometers on the belt, forearm, arm, and dumbell of 6 participants to identify if the barbell lifts were done correctly or incorrectly.
Training Data: https://d396qusza40orc.cloudfront.net/predmachlearn/pml-training.csv
Test Data: https://d396qusza40orc.cloudfront.net/predmachlearn/pml-testing.csv
Exploratory Data Analysis
In this step we will load the data and do some exploratory analysis to see for relationships between the data and possible predictors.
Load Data
library(caret)## Warning: package 'caret' was built under R version 3.4.3## Loading required package: lattice## Loading required package: ggplot2## Warning in as.POSIXlt.POSIXct(Sys.time()): unknown timezone 'zone/tz/2017c.
## 1.0/zoneinfo/Asia/Kolkata'library(stats)
library(ggplot2)
set.seed(1)file_url_training<-"https://d396qusza40orc.cloudfront.net/predmachlearn/pml-training.csv"
file_url_testing<-"https://d396qusza40orc.cloudfront.net/predmachlearn/pml-testing.csv"
#Dowload the files
training_file_name<-"pml-training.csv"
testing_file_name<-"pml-testing.csv"
if(!file.exists(training_file_name)){
download.file(file_url_training,training_file_name,method="curl")
}
if(!file.exists(testing_file_name)){
download.file(file_url_testing,testing_file_name,method="curl")
}
#Load the data
training<-read.csv(training_file_name)
testing<-read.csv(testing_file_name)
#Check data dimensions and names. Shown in the Appendix
dim(training)
dim(testing)
names(training)It looks like there are multiple measurements for three rotations (yaw, pitch, roll) taken from each of the sensors from the arm, belt, forearm and the dumbell.
Data Pre Processing
summary(training) #Shown in AppendixFrom the summary we can see that all the avg, standard deviation, variance, kurtosis, skewness, amplitude, min and max variables are either blank or have NAs so we can’t use those variables. So let’s create a subset dataset without these variables.Also, we will combine the two time stamps to create one complete time stamp for the dataset.
Also we can check for near zero variance variables and remove them since they will not add not value to he prediction algorithm.
#Remove the empty variables
index<-grep("avg|stddev|var|kurtosis|skewness|amplitude|min|max",names(training))
training_sub<-training[,-index]
testing_sub<-testing[,-index]
dim(training_sub)## [1] 19622 60#Create a complete time stamp
training_sub$full_time_stamp<-as.POSIXct(training_sub$raw_timestamp_part_1+training_sub$raw_timestamp_part_2/1000000,origin = "1970-01-01")
#Check for near zero variance variables.
nsv<-nearZeroVar(training_sub[,8:59],saveMetrics = TRUE)
any(nsv$zeroVar,nsv$nzv)## [1] FALSEThere are no near zero varation variables so we will keep all f them for now. Since the training dataset is big, we can create another data set for cross validation while keeping the test dataset as separate.
index_t<-createDataPartition(training_sub$classe,p=0.7,list = FALSE)
training_sub<-training_sub[index_t,]
validation_sub<-training_sub[-index_t,]
dim(training_sub)
dim(validation_sub)Exploratory Analysis
Let’s look at the data for any patterns that we can find. For this part we will look at the data for a single participant - Adelmo.
training_sub1<-training_sub[training_sub$user_name=="adelmo",8:60]
custom_plot<-function(x){
qplot(y=training_sub1[,x],color=training_sub1$classe,xlab="Index",ylab=names(training_sub1)[x])+labs(color="Classe")
}
plots<-lapply(1:52,custom_plot)#Shown in AppendixFrom the plots it we can see that almost all measurements variables from the belt sensor show a higher variation for the E class and clearly are good predictors. Similary measurements from dumbell do seprate class A and D from the other two classes and so on.
Pre Processing
The username, new_window etc variables do not add anything to the model so we will remove them in the next step before proceeding with the modelling
training_sub_final<-training_sub[,8:60]
validation_sub_final<-validation_sub[,8:60]
testing_sub_final<-testing_sub[,8:60]Prediction Model
Since this is a non linear classification problem we will try a couple of classification algorithms, namely Tree Classification and Random Forest.
Also, since the most of measurements from a sensor gives similar clusters for a class we maybe able to compress the data further. Therefore, we will also do Principal Component Analysis and apply the Randon Forest algorithmsm (since it takes a lot of time) with and without pca to see if they give same results.
Classification tree
model_class<-train(classe~.,method="rpart",data=training_sub_final)
print("Classification")## [1] "Classification"model_class$results## cp Accuracy Kappa AccuracySD KappaSD
## 1 0.03661886 0.5158174 0.37202950 0.02771903 0.04462356
## 2 0.05947174 0.4390471 0.24688630 0.06503062 0.10800011
## 3 0.11789238 0.3384894 0.08206845 0.04226522 0.06291225#Check the accuracy on the validation dataset
print("Classification accuracy on validation dataset")## [1] "Classification accuracy on validation dataset"confusionMatrix(validation_sub_final$classe,predict(model_class,validation_sub_final))$overall## Accuracy Kappa AccuracyLower AccuracyUpper AccuracyNull
## 0.5029183 0.3491525 0.4875171 0.5183154 0.5121595
## AccuracyPValue McnemarPValue
## 0.8851423 NaNThe accuracy of the classification tree both in and out of sample is around 50% which is very low. Let’s us look at random forest.
Random Forest
model_rf<-train(classe~.,method="rf",data=training_sub_final)
print("Random Forest without PCA")## [1] "Random Forest without PCA"model_rf$results## mtry Accuracy Kappa AccuracySD KappaSD
## 1 2 0.9883046 0.9852005 0.001891847 0.002388797
## 2 27 0.9890386 0.9861299 0.001663092 0.002101330
## 3 52 0.9805085 0.9753358 0.004137394 0.005233384#Check the accuracy on the validation dataset
print("Random Forest accuracy on validation dataset")## [1] "Random Forest accuracy on validation dataset"confusionMatrix(validation_sub_final$classe,predict(model_rf,validation_sub_final))$overall## Accuracy Kappa AccuracyLower AccuracyUpper AccuracyNull
## 1.0000000 1.0000000 0.9991033 1.0000000 0.2891537
## AccuracyPValue McnemarPValue
## 0.0000000 NaNctrl<-trainControl(preProcOptions = list(pcaComp=25))
model_rf_pca<-train(classe~.,method="rf",data=training_sub_final,preProcess="pca",trControl=ctrl)
print("Random Forest with PCA")## [1] "Random Forest with PCA"model_rf_pca$results## mtry Accuracy Kappa AccuracySD KappaSD
## 1 2 0.9618374 0.9517147 0.003381376 0.004283247
## 2 27 0.9418981 0.9264956 0.006392229 0.008044583
## 3 52 0.9421673 0.9268376 0.006599513 0.008304935#Check the accuracy on the validation dataset
print("Random Forest (with PCA) accuracy on validation dataset")## [1] "Random Forest (with PCA) accuracy on validation dataset"confusionMatrix(validation_sub_final$classe,predict(model_rf_pca,validation_sub_final))$overall## Accuracy Kappa AccuracyLower AccuracyUpper AccuracyNull
## 1.0000000 1.0000000 0.9991033 1.0000000 0.2891537
## AccuracyPValue McnemarPValue
## 0.0000000 NaNRandom Forest has an acuracy of 95%. However it takes a lot of time. Also, the accuracy dropped when used with PCA. Therefore, we will use the model without PCA.
Prediction of Test data
We will now use the Random Forest model (without PCA) to predict the class on the test dataset.
dim(testing_sub_final)## [1] 20 53pred_test<-predict(model_rf,testing_sub_final)
print("Random Forest prediction on test dataset")## [1] "Random Forest prediction on test dataset"pred_test## [1] B A B A A E D B A A B C B A E E A B B B
## Levels: A B C D EAppendix
#Dimensions and names of the training and test data sets
dim(training)## [1] 19622 160dim(testing)## [1] 20 160names(training)## [1] "X" "user_name"
## [3] "raw_timestamp_part_1" "raw_timestamp_part_2"
## [5] "cvtd_timestamp" "new_window"
## [7] "num_window" "roll_belt"
## [9] "pitch_belt" "yaw_belt"
## [11] "total_accel_belt" "kurtosis_roll_belt"
## [13] "kurtosis_picth_belt" "kurtosis_yaw_belt"
## [15] "skewness_roll_belt" "skewness_roll_belt.1"
## [17] "skewness_yaw_belt" "max_roll_belt"
## [19] "max_picth_belt" "max_yaw_belt"
## [21] "min_roll_belt" "min_pitch_belt"
## [23] "min_yaw_belt" "amplitude_roll_belt"
## [25] "amplitude_pitch_belt" "amplitude_yaw_belt"
## [27] "var_total_accel_belt" "avg_roll_belt"
## [29] "stddev_roll_belt" "var_roll_belt"
## [31] "avg_pitch_belt" "stddev_pitch_belt"
## [33] "var_pitch_belt" "avg_yaw_belt"
## [35] "stddev_yaw_belt" "var_yaw_belt"
## [37] "gyros_belt_x" "gyros_belt_y"
## [39] "gyros_belt_z" "accel_belt_x"
## [41] "accel_belt_y" "accel_belt_z"
## [43] "magnet_belt_x" "magnet_belt_y"
## [45] "magnet_belt_z" "roll_arm"
## [47] "pitch_arm" "yaw_arm"
## [49] "total_accel_arm" "var_accel_arm"
## [51] "avg_roll_arm" "stddev_roll_arm"
## [53] "var_roll_arm" "avg_pitch_arm"
## [55] "stddev_pitch_arm" "var_pitch_arm"
## [57] "avg_yaw_arm" "stddev_yaw_arm"
## [59] "var_yaw_arm" "gyros_arm_x"
## [61] "gyros_arm_y" "gyros_arm_z"
## [63] "accel_arm_x" "accel_arm_y"
## [65] "accel_arm_z" "magnet_arm_x"
## [67] "magnet_arm_y" "magnet_arm_z"
## [69] "kurtosis_roll_arm" "kurtosis_picth_arm"
## [71] "kurtosis_yaw_arm" "skewness_roll_arm"
## [73] "skewness_pitch_arm" "skewness_yaw_arm"
## [75] "max_roll_arm" "max_picth_arm"
## [77] "max_yaw_arm" "min_roll_arm"
## [79] "min_pitch_arm" "min_yaw_arm"
## [81] "amplitude_roll_arm" "amplitude_pitch_arm"
## [83] "amplitude_yaw_arm" "roll_dumbbell"
## [85] "pitch_dumbbell" "yaw_dumbbell"
## [87] "kurtosis_roll_dumbbell" "kurtosis_picth_dumbbell"
## [89] "kurtosis_yaw_dumbbell" "skewness_roll_dumbbell"
## [91] "skewness_pitch_dumbbell" "skewness_yaw_dumbbell"
## [93] "max_roll_dumbbell" "max_picth_dumbbell"
## [95] "max_yaw_dumbbell" "min_roll_dumbbell"
## [97] "min_pitch_dumbbell" "min_yaw_dumbbell"
## [99] "amplitude_roll_dumbbell" "amplitude_pitch_dumbbell"
## [101] "amplitude_yaw_dumbbell" "total_accel_dumbbell"
## [103] "var_accel_dumbbell" "avg_roll_dumbbell"
## [105] "stddev_roll_dumbbell" "var_roll_dumbbell"
## [107] "avg_pitch_dumbbell" "stddev_pitch_dumbbell"
## [109] "var_pitch_dumbbell" "avg_yaw_dumbbell"
## [111] "stddev_yaw_dumbbell" "var_yaw_dumbbell"
## [113] "gyros_dumbbell_x" "gyros_dumbbell_y"
## [115] "gyros_dumbbell_z" "accel_dumbbell_x"
## [117] "accel_dumbbell_y" "accel_dumbbell_z"
## [119] "magnet_dumbbell_x" "magnet_dumbbell_y"
## [121] "magnet_dumbbell_z" "roll_forearm"
## [123] "pitch_forearm" "yaw_forearm"
## [125] "kurtosis_roll_forearm" "kurtosis_picth_forearm"
## [127] "kurtosis_yaw_forearm" "skewness_roll_forearm"
## [129] "skewness_pitch_forearm" "skewness_yaw_forearm"
## [131] "max_roll_forearm" "max_picth_forearm"
## [133] "max_yaw_forearm" "min_roll_forearm"
## [135] "min_pitch_forearm" "min_yaw_forearm"
## [137] "amplitude_roll_forearm" "amplitude_pitch_forearm"
## [139] "amplitude_yaw_forearm" "total_accel_forearm"
## [141] "var_accel_forearm" "avg_roll_forearm"
## [143] "stddev_roll_forearm" "var_roll_forearm"
## [145] "avg_pitch_forearm" "stddev_pitch_forearm"
## [147] "var_pitch_forearm" "avg_yaw_forearm"
## [149] "stddev_yaw_forearm" "var_yaw_forearm"
## [151] "gyros_forearm_x" "gyros_forearm_y"
## [153] "gyros_forearm_z" "accel_forearm_x"
## [155] "accel_forearm_y" "accel_forearm_z"
## [157] "magnet_forearm_x" "magnet_forearm_y"
## [159] "magnet_forearm_z" "classe"#Summary of the initial traiing dataset
summary(training)## X user_name raw_timestamp_part_1 raw_timestamp_part_2
## Min. : 1 adelmo :3892 Min. :1.322e+09 Min. : 294
## 1st Qu.: 4906 carlitos:3112 1st Qu.:1.323e+09 1st Qu.:252912
## Median : 9812 charles :3536 Median :1.323e+09 Median :496380
## Mean : 9812 eurico :3070 Mean :1.323e+09 Mean :500656
## 3rd Qu.:14717 jeremy :3402 3rd Qu.:1.323e+09 3rd Qu.:751891
## Max. :19622 pedro :2610 Max. :1.323e+09 Max. :998801
##
## cvtd_timestamp new_window num_window roll_belt
## 28/11/2011 14:14: 1498 no :19216 Min. : 1.0 Min. :-28.90
## 05/12/2011 11:24: 1497 yes: 406 1st Qu.:222.0 1st Qu.: 1.10
## 30/11/2011 17:11: 1440 Median :424.0 Median :113.00
## 05/12/2011 11:25: 1425 Mean :430.6 Mean : 64.41
## 02/12/2011 14:57: 1380 3rd Qu.:644.0 3rd Qu.:123.00
## 02/12/2011 13:34: 1375 Max. :864.0 Max. :162.00
## (Other) :11007
## pitch_belt yaw_belt total_accel_belt kurtosis_roll_belt
## Min. :-55.8000 Min. :-180.00 Min. : 0.00 :19216
## 1st Qu.: 1.7600 1st Qu.: -88.30 1st Qu.: 3.00 #DIV/0! : 10
## Median : 5.2800 Median : -13.00 Median :17.00 -1.908453: 2
## Mean : 0.3053 Mean : -11.21 Mean :11.31 -0.016850: 1
## 3rd Qu.: 14.9000 3rd Qu.: 12.90 3rd Qu.:18.00 -0.021024: 1
## Max. : 60.3000 Max. : 179.00 Max. :29.00 -0.025513: 1
## (Other) : 391
## kurtosis_picth_belt kurtosis_yaw_belt skewness_roll_belt
## :19216 :19216 :19216
## #DIV/0! : 32 #DIV/0!: 406 #DIV/0! : 9
## 47.000000: 4 0.000000 : 4
## -0.150950: 3 0.422463 : 2
## -0.684748: 3 -0.003095: 1
## -1.750749: 3 -0.010002: 1
## (Other) : 361 (Other) : 389
## skewness_roll_belt.1 skewness_yaw_belt max_roll_belt max_picth_belt
## :19216 :19216 Min. :-94.300 Min. : 3.00
## #DIV/0! : 32 #DIV/0!: 406 1st Qu.:-88.000 1st Qu.: 5.00
## 0.000000 : 4 Median : -5.100 Median :18.00
## -2.156553: 3 Mean : -6.667 Mean :12.92
## -3.072669: 3 3rd Qu.: 18.500 3rd Qu.:19.00
## -6.324555: 3 Max. :180.000 Max. :30.00
## (Other) : 361 NA's :19216 NA's :19216
## max_yaw_belt min_roll_belt min_pitch_belt min_yaw_belt
## :19216 Min. :-180.00 Min. : 0.00 :19216
## -1.1 : 30 1st Qu.: -88.40 1st Qu.: 3.00 -1.1 : 30
## -1.4 : 29 Median : -7.85 Median :16.00 -1.4 : 29
## -1.2 : 26 Mean : -10.44 Mean :10.76 -1.2 : 26
## -0.9 : 24 3rd Qu.: 9.05 3rd Qu.:17.00 -0.9 : 24
## -1.3 : 22 Max. : 173.00 Max. :23.00 -1.3 : 22
## (Other): 275 NA's :19216 NA's :19216 (Other): 275
## amplitude_roll_belt amplitude_pitch_belt amplitude_yaw_belt
## Min. : 0.000 Min. : 0.000 :19216
## 1st Qu.: 0.300 1st Qu.: 1.000 #DIV/0!: 10
## Median : 1.000 Median : 1.000 0.00 : 12
## Mean : 3.769 Mean : 2.167 0.0000 : 384
## 3rd Qu.: 2.083 3rd Qu.: 2.000
## Max. :360.000 Max. :12.000
## NA's :19216 NA's :19216
## var_total_accel_belt avg_roll_belt stddev_roll_belt var_roll_belt
## Min. : 0.000 Min. :-27.40 Min. : 0.000 Min. : 0.000
## 1st Qu.: 0.100 1st Qu.: 1.10 1st Qu.: 0.200 1st Qu.: 0.000
## Median : 0.200 Median :116.35 Median : 0.400 Median : 0.100
## Mean : 0.926 Mean : 68.06 Mean : 1.337 Mean : 7.699
## 3rd Qu.: 0.300 3rd Qu.:123.38 3rd Qu.: 0.700 3rd Qu.: 0.500
## Max. :16.500 Max. :157.40 Max. :14.200 Max. :200.700
## NA's :19216 NA's :19216 NA's :19216 NA's :19216
## avg_pitch_belt stddev_pitch_belt var_pitch_belt avg_yaw_belt
## Min. :-51.400 Min. :0.000 Min. : 0.000 Min. :-138.300
## 1st Qu.: 2.025 1st Qu.:0.200 1st Qu.: 0.000 1st Qu.: -88.175
## Median : 5.200 Median :0.400 Median : 0.100 Median : -6.550
## Mean : 0.520 Mean :0.603 Mean : 0.766 Mean : -8.831
## 3rd Qu.: 15.775 3rd Qu.:0.700 3rd Qu.: 0.500 3rd Qu.: 14.125
## Max. : 59.700 Max. :4.000 Max. :16.200 Max. : 173.500
## NA's :19216 NA's :19216 NA's :19216 NA's :19216
## stddev_yaw_belt var_yaw_belt gyros_belt_x
## Min. : 0.000 Min. : 0.000 Min. :-1.040000
## 1st Qu.: 0.100 1st Qu.: 0.010 1st Qu.:-0.030000
## Median : 0.300 Median : 0.090 Median : 0.030000
## Mean : 1.341 Mean : 107.487 Mean :-0.005592
## 3rd Qu.: 0.700 3rd Qu.: 0.475 3rd Qu.: 0.110000
## Max. :176.600 Max. :31183.240 Max. : 2.220000
## NA's :19216 NA's :19216
## gyros_belt_y gyros_belt_z accel_belt_x accel_belt_y
## Min. :-0.64000 Min. :-1.4600 Min. :-120.000 Min. :-69.00
## 1st Qu.: 0.00000 1st Qu.:-0.2000 1st Qu.: -21.000 1st Qu.: 3.00
## Median : 0.02000 Median :-0.1000 Median : -15.000 Median : 35.00
## Mean : 0.03959 Mean :-0.1305 Mean : -5.595 Mean : 30.15
## 3rd Qu.: 0.11000 3rd Qu.:-0.0200 3rd Qu.: -5.000 3rd Qu.: 61.00
## Max. : 0.64000 Max. : 1.6200 Max. : 85.000 Max. :164.00
##
## accel_belt_z magnet_belt_x magnet_belt_y magnet_belt_z
## Min. :-275.00 Min. :-52.0 Min. :354.0 Min. :-623.0
## 1st Qu.:-162.00 1st Qu.: 9.0 1st Qu.:581.0 1st Qu.:-375.0
## Median :-152.00 Median : 35.0 Median :601.0 Median :-320.0
## Mean : -72.59 Mean : 55.6 Mean :593.7 Mean :-345.5
## 3rd Qu.: 27.00 3rd Qu.: 59.0 3rd Qu.:610.0 3rd Qu.:-306.0
## Max. : 105.00 Max. :485.0 Max. :673.0 Max. : 293.0
##
## roll_arm pitch_arm yaw_arm total_accel_arm
## Min. :-180.00 Min. :-88.800 Min. :-180.0000 Min. : 1.00
## 1st Qu.: -31.77 1st Qu.:-25.900 1st Qu.: -43.1000 1st Qu.:17.00
## Median : 0.00 Median : 0.000 Median : 0.0000 Median :27.00
## Mean : 17.83 Mean : -4.612 Mean : -0.6188 Mean :25.51
## 3rd Qu.: 77.30 3rd Qu.: 11.200 3rd Qu.: 45.8750 3rd Qu.:33.00
## Max. : 180.00 Max. : 88.500 Max. : 180.0000 Max. :66.00
##
## var_accel_arm avg_roll_arm stddev_roll_arm var_roll_arm
## Min. : 0.00 Min. :-166.67 Min. : 0.000 Min. : 0.000
## 1st Qu.: 9.03 1st Qu.: -38.37 1st Qu.: 1.376 1st Qu.: 1.898
## Median : 40.61 Median : 0.00 Median : 5.702 Median : 32.517
## Mean : 53.23 Mean : 12.68 Mean : 11.201 Mean : 417.264
## 3rd Qu.: 75.62 3rd Qu.: 76.33 3rd Qu.: 14.921 3rd Qu.: 222.647
## Max. :331.70 Max. : 163.33 Max. :161.964 Max. :26232.208
## NA's :19216 NA's :19216 NA's :19216 NA's :19216
## avg_pitch_arm stddev_pitch_arm var_pitch_arm avg_yaw_arm
## Min. :-81.773 Min. : 0.000 Min. : 0.000 Min. :-173.440
## 1st Qu.:-22.770 1st Qu.: 1.642 1st Qu.: 2.697 1st Qu.: -29.198
## Median : 0.000 Median : 8.133 Median : 66.146 Median : 0.000
## Mean : -4.901 Mean :10.383 Mean : 195.864 Mean : 2.359
## 3rd Qu.: 8.277 3rd Qu.:16.327 3rd Qu.: 266.576 3rd Qu.: 38.185
## Max. : 75.659 Max. :43.412 Max. :1884.565 Max. : 152.000
## NA's :19216 NA's :19216 NA's :19216 NA's :19216
## stddev_yaw_arm var_yaw_arm gyros_arm_x
## Min. : 0.000 Min. : 0.000 Min. :-6.37000
## 1st Qu.: 2.577 1st Qu.: 6.642 1st Qu.:-1.33000
## Median : 16.682 Median : 278.309 Median : 0.08000
## Mean : 22.270 Mean : 1055.933 Mean : 0.04277
## 3rd Qu.: 35.984 3rd Qu.: 1294.850 3rd Qu.: 1.57000
## Max. :177.044 Max. :31344.568 Max. : 4.87000
## NA's :19216 NA's :19216
## gyros_arm_y gyros_arm_z accel_arm_x accel_arm_y
## Min. :-3.4400 Min. :-2.3300 Min. :-404.00 Min. :-318.0
## 1st Qu.:-0.8000 1st Qu.:-0.0700 1st Qu.:-242.00 1st Qu.: -54.0
## Median :-0.2400 Median : 0.2300 Median : -44.00 Median : 14.0
## Mean :-0.2571 Mean : 0.2695 Mean : -60.24 Mean : 32.6
## 3rd Qu.: 0.1400 3rd Qu.: 0.7200 3rd Qu.: 84.00 3rd Qu.: 139.0
## Max. : 2.8400 Max. : 3.0200 Max. : 437.00 Max. : 308.0
##
## accel_arm_z magnet_arm_x magnet_arm_y magnet_arm_z
## Min. :-636.00 Min. :-584.0 Min. :-392.0 Min. :-597.0
## 1st Qu.:-143.00 1st Qu.:-300.0 1st Qu.: -9.0 1st Qu.: 131.2
## Median : -47.00 Median : 289.0 Median : 202.0 Median : 444.0
## Mean : -71.25 Mean : 191.7 Mean : 156.6 Mean : 306.5
## 3rd Qu.: 23.00 3rd Qu.: 637.0 3rd Qu.: 323.0 3rd Qu.: 545.0
## Max. : 292.00 Max. : 782.0 Max. : 583.0 Max. : 694.0
##
## kurtosis_roll_arm kurtosis_picth_arm kurtosis_yaw_arm skewness_roll_arm
## :19216 :19216 :19216 :19216
## #DIV/0! : 78 #DIV/0! : 80 #DIV/0! : 11 #DIV/0! : 77
## -0.02438: 1 -0.00484: 1 0.55844 : 2 -0.00051: 1
## -0.04190: 1 -0.01311: 1 0.65132 : 2 -0.00696: 1
## -0.05051: 1 -0.02967: 1 -0.01548: 1 -0.01884: 1
## -0.05695: 1 -0.07394: 1 -0.01749: 1 -0.03359: 1
## (Other) : 324 (Other) : 322 (Other) : 389 (Other) : 325
## skewness_pitch_arm skewness_yaw_arm max_roll_arm max_picth_arm
## :19216 :19216 Min. :-73.100 Min. :-173.000
## #DIV/0! : 80 #DIV/0! : 11 1st Qu.: -0.175 1st Qu.: -1.975
## -0.00184: 1 -1.62032: 2 Median : 4.950 Median : 23.250
## -0.01185: 1 0.55053 : 2 Mean : 11.236 Mean : 35.751
## -0.01247: 1 -0.00311: 1 3rd Qu.: 26.775 3rd Qu.: 95.975
## -0.02063: 1 -0.00562: 1 Max. : 85.500 Max. : 180.000
## (Other) : 322 (Other) : 389 NA's :19216 NA's :19216
## max_yaw_arm min_roll_arm min_pitch_arm min_yaw_arm
## Min. : 4.00 Min. :-89.10 Min. :-180.00 Min. : 1.00
## 1st Qu.:29.00 1st Qu.:-41.98 1st Qu.: -72.62 1st Qu.: 8.00
## Median :34.00 Median :-22.45 Median : -33.85 Median :13.00
## Mean :35.46 Mean :-21.22 Mean : -33.92 Mean :14.66
## 3rd Qu.:41.00 3rd Qu.: 0.00 3rd Qu.: 0.00 3rd Qu.:19.00
## Max. :65.00 Max. : 66.40 Max. : 152.00 Max. :38.00
## NA's :19216 NA's :19216 NA's :19216 NA's :19216
## amplitude_roll_arm amplitude_pitch_arm amplitude_yaw_arm
## Min. : 0.000 Min. : 0.000 Min. : 0.00
## 1st Qu.: 5.425 1st Qu.: 9.925 1st Qu.:13.00
## Median : 28.450 Median : 54.900 Median :22.00
## Mean : 32.452 Mean : 69.677 Mean :20.79
## 3rd Qu.: 50.960 3rd Qu.:115.175 3rd Qu.:28.75
## Max. :119.500 Max. :360.000 Max. :52.00
## NA's :19216 NA's :19216 NA's :19216
## roll_dumbbell pitch_dumbbell yaw_dumbbell
## Min. :-153.71 Min. :-149.59 Min. :-150.871
## 1st Qu.: -18.49 1st Qu.: -40.89 1st Qu.: -77.644
## Median : 48.17 Median : -20.96 Median : -3.324
## Mean : 23.84 Mean : -10.78 Mean : 1.674
## 3rd Qu.: 67.61 3rd Qu.: 17.50 3rd Qu.: 79.643
## Max. : 153.55 Max. : 149.40 Max. : 154.952
##
## kurtosis_roll_dumbbell kurtosis_picth_dumbbell kurtosis_yaw_dumbbell
## :19216 :19216 :19216
## #DIV/0!: 5 #DIV/0!: 2 #DIV/0!: 406
## -0.2583: 2 -0.5464: 2
## -0.3705: 2 -0.9334: 2
## -0.5855: 2 -2.0833: 2
## -2.0851: 2 -2.0851: 2
## (Other): 393 (Other): 396
## skewness_roll_dumbbell skewness_pitch_dumbbell skewness_yaw_dumbbell
## :19216 :19216 :19216
## #DIV/0!: 4 -0.2328: 2 #DIV/0!: 406
## -0.9324: 2 -0.3521: 2
## 0.1110 : 2 -0.7036: 2
## 1.0312 : 2 0.1090 : 2
## -0.0082: 1 1.0326 : 2
## (Other): 395 (Other): 396
## max_roll_dumbbell max_picth_dumbbell max_yaw_dumbbell min_roll_dumbbell
## Min. :-70.10 Min. :-112.90 :19216 Min. :-149.60
## 1st Qu.:-27.15 1st Qu.: -66.70 -0.6 : 20 1st Qu.: -59.67
## Median : 14.85 Median : 40.05 0.2 : 19 Median : -43.55
## Mean : 13.76 Mean : 32.75 -0.8 : 18 Mean : -41.24
## 3rd Qu.: 50.58 3rd Qu.: 133.22 -0.3 : 16 3rd Qu.: -25.20
## Max. :137.00 Max. : 155.00 -0.2 : 15 Max. : 73.20
## NA's :19216 NA's :19216 (Other): 318 NA's :19216
## min_pitch_dumbbell min_yaw_dumbbell amplitude_roll_dumbbell
## Min. :-147.00 :19216 Min. : 0.00
## 1st Qu.: -91.80 -0.6 : 20 1st Qu.: 14.97
## Median : -66.15 0.2 : 19 Median : 35.05
## Mean : -33.18 -0.8 : 18 Mean : 55.00
## 3rd Qu.: 21.20 -0.3 : 16 3rd Qu.: 81.04
## Max. : 120.90 -0.2 : 15 Max. :256.48
## NA's :19216 (Other): 318 NA's :19216
## amplitude_pitch_dumbbell amplitude_yaw_dumbbell total_accel_dumbbell
## Min. : 0.00 :19216 Min. : 0.00
## 1st Qu.: 17.06 #DIV/0!: 5 1st Qu.: 4.00
## Median : 41.73 0.00 : 401 Median :10.00
## Mean : 65.93 Mean :13.72
## 3rd Qu.: 99.55 3rd Qu.:19.00
## Max. :273.59 Max. :58.00
## NA's :19216
## var_accel_dumbbell avg_roll_dumbbell stddev_roll_dumbbell
## Min. : 0.000 Min. :-128.96 Min. : 0.000
## 1st Qu.: 0.378 1st Qu.: -12.33 1st Qu.: 4.639
## Median : 1.000 Median : 48.23 Median : 12.204
## Mean : 4.388 Mean : 23.86 Mean : 20.761
## 3rd Qu.: 3.434 3rd Qu.: 64.37 3rd Qu.: 26.356
## Max. :230.428 Max. : 125.99 Max. :123.778
## NA's :19216 NA's :19216 NA's :19216
## var_roll_dumbbell avg_pitch_dumbbell stddev_pitch_dumbbell
## Min. : 0.00 Min. :-70.73 Min. : 0.000
## 1st Qu.: 21.52 1st Qu.:-42.00 1st Qu.: 3.482
## Median : 148.95 Median :-19.91 Median : 8.089
## Mean : 1020.27 Mean :-12.33 Mean :13.147
## 3rd Qu.: 694.65 3rd Qu.: 13.21 3rd Qu.:19.238
## Max. :15321.01 Max. : 94.28 Max. :82.680
## NA's :19216 NA's :19216 NA's :19216
## var_pitch_dumbbell avg_yaw_dumbbell stddev_yaw_dumbbell
## Min. : 0.00 Min. :-117.950 Min. : 0.000
## 1st Qu.: 12.12 1st Qu.: -76.696 1st Qu.: 3.885
## Median : 65.44 Median : -4.505 Median : 10.264
## Mean : 350.31 Mean : 0.202 Mean : 16.647
## 3rd Qu.: 370.11 3rd Qu.: 71.234 3rd Qu.: 24.674
## Max. :6836.02 Max. : 134.905 Max. :107.088
## NA's :19216 NA's :19216 NA's :19216
## var_yaw_dumbbell gyros_dumbbell_x gyros_dumbbell_y
## Min. : 0.00 Min. :-204.0000 Min. :-2.10000
## 1st Qu.: 15.09 1st Qu.: -0.0300 1st Qu.:-0.14000
## Median : 105.35 Median : 0.1300 Median : 0.03000
## Mean : 589.84 Mean : 0.1611 Mean : 0.04606
## 3rd Qu.: 608.79 3rd Qu.: 0.3500 3rd Qu.: 0.21000
## Max. :11467.91 Max. : 2.2200 Max. :52.00000
## NA's :19216
## gyros_dumbbell_z accel_dumbbell_x accel_dumbbell_y accel_dumbbell_z
## Min. : -2.380 Min. :-419.00 Min. :-189.00 Min. :-334.00
## 1st Qu.: -0.310 1st Qu.: -50.00 1st Qu.: -8.00 1st Qu.:-142.00
## Median : -0.130 Median : -8.00 Median : 41.50 Median : -1.00
## Mean : -0.129 Mean : -28.62 Mean : 52.63 Mean : -38.32
## 3rd Qu.: 0.030 3rd Qu.: 11.00 3rd Qu.: 111.00 3rd Qu.: 38.00
## Max. :317.000 Max. : 235.00 Max. : 315.00 Max. : 318.00
##
## magnet_dumbbell_x magnet_dumbbell_y magnet_dumbbell_z roll_forearm
## Min. :-643.0 Min. :-3600 Min. :-262.00 Min. :-180.0000
## 1st Qu.:-535.0 1st Qu.: 231 1st Qu.: -45.00 1st Qu.: -0.7375
## Median :-479.0 Median : 311 Median : 13.00 Median : 21.7000
## Mean :-328.5 Mean : 221 Mean : 46.05 Mean : 33.8265
## 3rd Qu.:-304.0 3rd Qu.: 390 3rd Qu.: 95.00 3rd Qu.: 140.0000
## Max. : 592.0 Max. : 633 Max. : 452.00 Max. : 180.0000
##
## pitch_forearm yaw_forearm kurtosis_roll_forearm
## Min. :-72.50 Min. :-180.00 :19216
## 1st Qu.: 0.00 1st Qu.: -68.60 #DIV/0!: 84
## Median : 9.24 Median : 0.00 -0.8079: 2
## Mean : 10.71 Mean : 19.21 -0.9169: 2
## 3rd Qu.: 28.40 3rd Qu.: 110.00 -0.0227: 1
## Max. : 89.80 Max. : 180.00 -0.0359: 1
## (Other): 316
## kurtosis_picth_forearm kurtosis_yaw_forearm skewness_roll_forearm
## :19216 :19216 :19216
## #DIV/0!: 85 #DIV/0!: 406 #DIV/0!: 83
## -0.0073: 1 -0.1912: 2
## -0.0442: 1 -0.4126: 2
## -0.0489: 1 -0.0004: 1
## -0.0523: 1 -0.0013: 1
## (Other): 317 (Other): 317
## skewness_pitch_forearm skewness_yaw_forearm max_roll_forearm
## :19216 :19216 Min. :-66.60
## #DIV/0!: 85 #DIV/0!: 406 1st Qu.: 0.00
## 0.0000 : 4 Median : 26.80
## -0.6992: 2 Mean : 24.49
## -0.0113: 1 3rd Qu.: 45.95
## -0.0131: 1 Max. : 89.80
## (Other): 313 NA's :19216
## max_picth_forearm max_yaw_forearm min_roll_forearm min_pitch_forearm
## Min. :-151.00 :19216 Min. :-72.500 Min. :-180.00
## 1st Qu.: 0.00 #DIV/0!: 84 1st Qu.: -6.075 1st Qu.:-175.00
## Median : 113.00 -1.2 : 32 Median : 0.000 Median : -61.00
## Mean : 81.49 -1.3 : 31 Mean : -0.167 Mean : -57.57
## 3rd Qu.: 174.75 -1.4 : 24 3rd Qu.: 12.075 3rd Qu.: 0.00
## Max. : 180.00 -1.5 : 24 Max. : 62.100 Max. : 167.00
## NA's :19216 (Other): 211 NA's :19216 NA's :19216
## min_yaw_forearm amplitude_roll_forearm amplitude_pitch_forearm
## :19216 Min. : 0.000 Min. : 0.0
## #DIV/0!: 84 1st Qu.: 1.125 1st Qu.: 2.0
## -1.2 : 32 Median : 17.770 Median : 83.7
## -1.3 : 31 Mean : 24.653 Mean :139.1
## -1.4 : 24 3rd Qu.: 39.875 3rd Qu.:350.0
## -1.5 : 24 Max. :126.000 Max. :360.0
## (Other): 211 NA's :19216 NA's :19216
## amplitude_yaw_forearm total_accel_forearm var_accel_forearm
## :19216 Min. : 0.00 Min. : 0.000
## #DIV/0!: 84 1st Qu.: 29.00 1st Qu.: 6.759
## 0.00 : 322 Median : 36.00 Median : 21.165
## Mean : 34.72 Mean : 33.502
## 3rd Qu.: 41.00 3rd Qu.: 51.240
## Max. :108.00 Max. :172.606
## NA's :19216
## avg_roll_forearm stddev_roll_forearm var_roll_forearm
## Min. :-177.234 Min. : 0.000 Min. : 0.00
## 1st Qu.: -0.909 1st Qu.: 0.428 1st Qu.: 0.18
## Median : 11.172 Median : 8.030 Median : 64.48
## Mean : 33.165 Mean : 41.986 Mean : 5274.10
## 3rd Qu.: 107.132 3rd Qu.: 85.373 3rd Qu.: 7289.08
## Max. : 177.256 Max. :179.171 Max. :32102.24
## NA's :19216 NA's :19216 NA's :19216
## avg_pitch_forearm stddev_pitch_forearm var_pitch_forearm
## Min. :-68.17 Min. : 0.000 Min. : 0.000
## 1st Qu.: 0.00 1st Qu.: 0.336 1st Qu.: 0.113
## Median : 12.02 Median : 5.516 Median : 30.425
## Mean : 11.79 Mean : 7.977 Mean : 139.593
## 3rd Qu.: 28.48 3rd Qu.:12.866 3rd Qu.: 165.532
## Max. : 72.09 Max. :47.745 Max. :2279.617
## NA's :19216 NA's :19216 NA's :19216
## avg_yaw_forearm stddev_yaw_forearm var_yaw_forearm gyros_forearm_x
## Min. :-155.06 Min. : 0.000 Min. : 0.00 Min. :-22.000
## 1st Qu.: -26.26 1st Qu.: 0.524 1st Qu.: 0.27 1st Qu.: -0.220
## Median : 0.00 Median : 24.743 Median : 612.21 Median : 0.050
## Mean : 18.00 Mean : 44.854 Mean : 4639.85 Mean : 0.158
## 3rd Qu.: 85.79 3rd Qu.: 85.817 3rd Qu.: 7368.41 3rd Qu.: 0.560
## Max. : 169.24 Max. :197.508 Max. :39009.33 Max. : 3.970
## NA's :19216 NA's :19216 NA's :19216
## gyros_forearm_y gyros_forearm_z accel_forearm_x accel_forearm_y
## Min. : -7.02000 Min. : -8.0900 Min. :-498.00 Min. :-632.0
## 1st Qu.: -1.46000 1st Qu.: -0.1800 1st Qu.:-178.00 1st Qu.: 57.0
## Median : 0.03000 Median : 0.0800 Median : -57.00 Median : 201.0
## Mean : 0.07517 Mean : 0.1512 Mean : -61.65 Mean : 163.7
## 3rd Qu.: 1.62000 3rd Qu.: 0.4900 3rd Qu.: 76.00 3rd Qu.: 312.0
## Max. :311.00000 Max. :231.0000 Max. : 477.00 Max. : 923.0
##
## accel_forearm_z magnet_forearm_x magnet_forearm_y magnet_forearm_z
## Min. :-446.00 Min. :-1280.0 Min. :-896.0 Min. :-973.0
## 1st Qu.:-182.00 1st Qu.: -616.0 1st Qu.: 2.0 1st Qu.: 191.0
## Median : -39.00 Median : -378.0 Median : 591.0 Median : 511.0
## Mean : -55.29 Mean : -312.6 Mean : 380.1 Mean : 393.6
## 3rd Qu.: 26.00 3rd Qu.: -73.0 3rd Qu.: 737.0 3rd Qu.: 653.0
## Max. : 291.00 Max. : 672.0 Max. :1480.0 Max. :1090.0
##
## classe
## A:5580
## B:3797
## C:3422
## D:3216
## E:3607
##
## #Dimensions of the final subsets for training, validation and test data sets
dim(training_sub_final)## [1] 13737 53dim(validation_sub_final)## [1] 4112 53dim(testing_sub_final)## [1] 20 53#Plots of the measurements in the training dataset against the class for one participant.
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